Proceedings, The 2014 ASEE North Midwest Section Conference, October 16‐17, 2014, Iowa City, IA. ASEE‐NWMSC2014‐1C2
Using design hierarchy in a linear circuits class to illustrate
the scientific method as a human invention.
Dr. Douglas De Boer, PE
Dordt College, Sioux Center, Iowa
Abstract
There are various ways to classify academic studies. One might make a “two cultures” division,
separating academic studies into the humanities and sciences. Or one might have three divisions:
humanities, social sciences, and natural sciences. Or one might choose to classify academic
studies along the lines of traditional academic disciplines such as theology, law, art, music,
economics, social studies, languages, political studies, history, psychology, biology, physics,
chemistry, math, etc. In our era of global commerce, where does engineering fit in these types of
classification? What should engineers study? More fundamentally, why should engineers study
science?
In a 2008 presidential debate, candidate Barack Obama said that, “Ensuring that the U.S.
continues to lead the world in science and technology will be a central priority for my
administration.” At the same debate, Candidate John McCain said that public policy, “should be
based upon sound science.”1 Within the field of engineering education, there are those who look
to scientific research on the topic of engineering education as key to achieving meaningful
improvements to engineering education.2 Within the general public there are those who might
say they “believe in global warming” or “evolution,” or some other topic of current interest
having a rather obvious basis in science. Why is there such general agreement that science
should be foundational in so many aspects of life, including engineering education?
Scientific theories are human formulations intended to describe and predict the behavior of the
natural world around us. Engineering work relies on scientific theories to be sure, but also on
many other academic disciplines. To train engineering students as “renaissance people” requires
that our students understand engineering as a multidisciplinary subject and a human endeavor.
Any engineering course ought to help students understand the breadth and depth of engineering
as well as the foundational role of science. This paper illustrates some examples of how this can
be done within a linear circuits class. Hopefully by seeing an example, the reader can generalize
the ideas to other engineering courses.
The hierarchical structure of engineering subjects, and specifically, linear circuits, naturally lends
itself to an illustration of how the science of linear circuits is humanly constructed. Some
specific aspects of the scientific method that can be elaborated on in the context of linear circuits
are the hierarchical nature of the scientific method, the axiomatic foundation of these hierarchies,
the limited scope of scientific theories and its utilitarian goals, essentially to predict the future if
given enough of the right information about the past and present. In contrast, the universe does
not exist in hierarchies, it is wholistic, and always has unpredictable aspects. Linear circuits are
also wholistic. When constructed and actually used they have limitations and even in some cases
unpredicted behaviors which the scientific theories of linear circuits do not fully explain. Such
understanding of the scientific method as a human invention is essential to relating ones
1 engineering (or science) to the culture around us, so that our work is responsive to real needs and
is recognizably beneficial.
Science and Engineering Defined
A dictionary definition of science is, “The intellectual and practical activity encompassing the
systematic study of the structure and behavior of the physical and natural world through
observation and experiment.”3. The same dictionary defines the scientific method as, “consisting
in systematic observation, measurement, and experiment, and the formulation, testing, and
modification of hypotheses.”4 These definitions of science and the scientific method do indeed
make reasonable sense of the statements of President Obama, John McCain, and others.
Obviously, these people considered science and the scientific method as knowledge and
principles used by people to bring about a desirable future. The importance of applying science
in these contexts rests in its accepted utilitarian value. People could make other choices. For
example, someone might advocate that public policy, or some other matter, should be based
upon religion instead of, “sound science.” Or one might choose to base some matter upon
economics or aesthetics instead of, “sound science.” There are, of course, many possible
fundamental bases upon which to rest a decision. The choice of a basis, or some weighting of
several bases, is a humanly made choice.
Consider now how these definitions and applications of science relate to engineering. A
dictionary definition of engineering is, “The branch of science and technology concerned with
the design, building, and use of engines. . .” (The word “engineering” might also refer to certain
works or an occupation or an artful design to bring something to fruition.)5 The concept of an
“engine” in this definition is intended to be taken broadly, meaning to include machines,
structures, and various technically complicated physical systems, etc. Although the concept of
engineering as having to do with the design of “engines” is rather memorable, the true core of
this definition of engineering is that it is a branch of science and technology, or in other words, it
involves the application of the scientific method, toward the design, building and use of
“engines.” This definition highlights science to such a degree as to imply that the application of
the scientific method is practically the only activity involved in doing engineering! It is no
wonder that in light of this overly-narrow definition of engineering the public has difficulty
understanding what engineers do. Indeed, engineers get involved in government and politics in
order to create regulations and standards, create building codes and other quisi-legal entities.
They are also employed by government to standardize the weights and measures that are the
basis of all commerce (e.g. Bureau International des Poeds et Mesures in France, and The
National Institute of Standards and Technology in the U. S.). They write and provide expertise
on patents, and in sort, they do quite a lot of work that goes beyond simply making hypotheses
and testing them (the scientific method) and also goes beyond even a generously broad
interpretation of, “designing, building, and using engines.” The full breadth of engineering
activities is rooted in a response to the technological desires of a culture. In order to respond
appropriately within a cultural context, engineers need a reasonable breadth of studies in all
academic disciplines, with a recognition that the natural sciences have a foundational role to the
work of engineers.
2 In their university courses, engineering students should become aware (if they are not already
aware) of the cultural motivation behind doing engineering work. It is in the context of a
relationship with the culture they are working in that engineering students will find a sense of joy
and fulfillment in their studies. Merely “designing, building, and using engines” for no
particular purpose offers little spiritual enrichment beyond the aesthetic satisfactions of the
sounds, textures, and other characteristics of “engines” themselves. While that narrow aesthetic
satisfaction may be adequate for some students, a more full-orbed concept of engineering work
will bring significantly more satisfaction for most students.
Teaching Linear Circuits
Most engineering courses rely on hierarchies of knowledge, and a linear circuits course is no
exception. By discussing hierarchies with the students one can draw attention to the human
activity that organized the body of knowledge (science) used in the course. A key concept that
needs to be communicated to students is that science, as a body of knowledge, is a result of
human activity. Humans, being what we are, do not come up with a perfect body of knowledge
on a first attempt. Human activity itself is also not exclusively scientific, perhaps even if we are
tying to produce a scientific experiment. In our choices of what to study and what not to study,
and in what hypotheses we choose to consider, and even in our choices of what evidence is
required to prove a hypothesis, humans make incremental progress as time passes, with
occasional mistakes included. These choices and decisions are themselves not scientific. They
are influenced by economic conditions and social opportunities, and also fundamental belief
structures, including conceptions of reality. In some cases the choice of what to study can
possibly even be influenced by fads and traditions. Helping students understand this helps
students distinguish between various conceptions of truth and cultural biases. This point can be
illustrated by an example showing how we abstract reality in order to create a hypotheses for
scientific investigation.
Scientific Abstraction Exemplified.
Imagine that the designer of an automobile says, “The electrical consumption of this car needs to
be reduced.” (Perhaps the alternator is not large enough to supply the present load and prior
decision-making has eliminated the possibility of upgrading to a larger alternator.) At this point,
in order to gain an understanding of where electrical consumption might be reduced, the engineer
might make in inventory of the current consumption of the various parts of the automobile. As
simple as this process might be, the values of the engineer will come into play. For example, the
car’s electrical loads might be divided into categories such as, lighting system, ignition system,
and everything else. But why not instead divide the categories into entertainment systems, safety
systems, and motive systems? The choice of categories is inherently non-scientific and
expressive of what the engineer values. An engineer who values economy of operation would
likely make a different choice of hierarchies and categories than an engineer who values the
aesthetic aspects of the car. An engineer concerned with the ultimate environmental impact of
the car might make still a different choice of hierarchy and categories.
3 One might argue that none of the categorizations in the above example are detailed enough.
Indeed, one can make more and different categories to get a more detailed perspective of the
situation. For example, within the “lighting” category, one could itemize “exterior,” “cabin,”
and “other lights.” Then within the “exterior” category one could itemize, “headlights,” “tail
lights,” “turn signals,” etc. There is practically no limit to the amount of detail one could
imagine itemizing in a hierarchical fashion. (The lights could be further classified by high and
low beam, color, incandescent vs. LED, etc. Incandescent lamps can be categorized by base
styles, internal gases, filament metallurgy, etc. and etc.) As more and more levels are added to
the hierarchy and as more categories are introduced, the hierarchy more completely characterizes
the electrical consumption of the car. The picture revealed by the hierarchy becomes a more
wholistic representation of the real situation. However, as a matter of utility and economy, the
engineer will use as few hierarchical levels and categories as are practical. Engineers must
deliberately omit some, or even a lot of detail from consideration. This is necessary in order to
focus attention on the need at hand. The choices of what to include and what to omit from our
attention are not scientifically made choices. Science comes after these prior choices of
hierarchies and categories are made.
When the final decisions are made and the product (the automobile in this example) is built, the
actual behavior of the product is wholistic. That is, the product acts as nature would have it act,
not necessarily as the engineering predicted. It is possible that the abstractions (what to consider
and what to omit) and the hierarchies used in the engineering were not adequately descriptive to
achieve the desired final behavior.
Abstraction, then, is the human process of identifying patterns in real situations by paying
attention to only a small but relevant portion of the available detail. The scientific method is a
process based upon a prior abstraction which is humanly invented. In this sense, science, the
scientific method are just some of the types of activities engineers engage in. An important
human activity that comes prior to doing science is the process of abstraction. In any process of
abstraction important expressions of value come into play.
Some Hierarchies in Linear Circuits
Most linear circuits courses start with a chapter or two of basic definitions of electrical quantities
such as current, voltage, electrical power, resistance, nodes, branches, etc. Students need to
realize that all of these definitions are culturally constructed and not simply handed down to us,
as if nature could talk.
Consider the definition of current, as might typically be encountered in a linear circuits course.
Any linear circuits textbook definition will suffice for our consideration since they are all
similar. For example, Hayt, Kermmerly and Durbin’s textbook states, “We define the current at
a specific point and flowing in a specified direction as the instantaneous rate at with net positive
charge is moving past that point in the specified direction.”6 One could introduce this definition
by asking students to define the current flow in a river. Students will have various conceptions
4 of this concept. For example, a student familiar with river navigation will be likely to discuss the
speed at which the surface of the water moves relative to the surrounding landscape. Indeed,
knowing the “current” in the river is, say, 3 miles-per-hour, is very useful knowledge for
navigating the river. However a student concerned with water resources management and
conservation might be more interested in the volume-rate of the flow of the river, say in gallonsper-hour. This conception of the “current” in the river makes it easier to understand the impact
of tributaries on the river, and the impact on the river of pollution from the tributaries. The two
different conceptual definitions of the current flow in a river are not reducible to one definition.
Factors such as the width and depth and the velocity profile within the river need to be known to
convert from one to the other, and these factors vary from one situation to another.
By discussing these basic definitions one can show how the definition of electrical current, as
presented in the textbook, is rooted in a cultural desire to apply electrical circuits to achieve
certain technologically-rooted desires (e.g. lighting, communication, transportation, etc.) Given
different goals, a different definition of electrical current could conceivably be more appropriate,
even if a different definition would be highly inappropriate for the linear circuits course!
However, for clarity we typically give different names to different definitions or conceptions of a
quantity. For example, in a solid-state devices course current density may be much more useful
than current flowing “past a point.” The definitions themselves are not scientifically proven
hypotheses. Rather, they are axiomatic human inventions with considerable utility. They arise
out of a process of abstraction.
After basic definitions are presented in a linear circuits course, some theorems or laws, such as
Kirchhoff’s Current and Voltage Laws, are presented. This is another humanly invented layer of
abstraction. These theorems can be proven via the scientific method, but the formulation of the
original hypotheses are humanly devised and rooted in utilitarian goals.
The linear circuits course proceeds through a list of increasingly abstract hierarchically
structured theorems and laws. Typically these would include superposition, Thevenin’s and
Norton’s theorems, nodal and mesh analysis, inductors and capacitors, phasors, and Fourier
Series. Supplementing the textbook with the cultural-historical concepts behind these humanly
invented theories and methods makes the course more interesting and fulfilling, giving students
motivation for further study.
Note that in electrical technology courses (in contrast to engineering courses) a different
hierarchy of knowledge is usually applied to this subject. It is usually organized around the type
of circuit encountered, such as DC or resistive circuits, electromagnetism, and AC circuits
(meaning sinusoidal circuits). An expression of this hierarchy might be found in the table of
contents of a typical textbook. A different ultimate goal for the utility of the course has resulted
in a different hierarchy of knowledge. (One evidence of this could be the table of contents of an
engineering technology textbook on circuits, for a specific example, the textbook by Robins and
Miller could be taken as typical of the genre.7)
5 The foundational role of science in engineering
Recall the earlier example of an engineer desiring to reduce the electrical consumption of an
automobile. Table 1 below expresses a possible example hierarchy that might relate to the
situation.
Table 1. Example of Hierarchy
A Hierarchy
 (One could imagine more over-arching
categories in higher levels of hierarchy.)
Transportation system
(including air, rail, truck, auto, ship. . . )
Road and highway system
Automobile
Electrical system in an automobile
Lighting system in an automobile
Tail light system
Right-turn indicator
flasher for turn indicator
Bi-metallic element in electro-mechanical turn
signal flasher
Contact point on bi-metalic element in turn
signal flasher
 (One could imagine even more detail by
adding lower levels of hierarchy.)
Other items “at the same level”
Utility distribution systems (water, electricity)
shipping lanes, air-traffic control
truck, ship, airplane
fuel system, suspension, exhaust, engine
ignition system, entertainment system
headlights, courtesy lights
parking lights, license plate light,
turn signal switch, turn signal wiring harness
bi-metallic heater in electro-mechanical turn
signal flasher
anchor for bi-metallic element, sound resonator
attached to bi-metallic element
Observe that as one moves up in the hierarchy the straight-forward application of the scientific
method to answer questions becomes increasingly difficult. What makes a transportation system
good? For that matter, what makes an automobile good? Different people will value different
aspects.
Conversely, as one moves down the levels of the hierarchy the design issues become further
abstracted from the ultimate cultural utility of the engineering work done. Designing a highly
efficient contact point for a bi-metallic-type turn signal flasher hardly seems culturally important
compared to designing a transportation system. Yet the design of internal parts in the turn signal
flasher is an enabler of the ultimate cultural objective.
At the lower levels of the hierarchy the application of the scientific method becomes more
obvious. What makes a contact point good? Without a whole lot of debate, one person or a
small team of people can propose a few hypotheses and extensively test them. This is the sense
in which science plays a foundational role in engineering design.
6 Conclusion
In engineering work, science and the scientific method have their most significant roles at lower
levels in the hierarchy of the design. In that sense, science is foundational to engineering design.
On the other hand, science is not the final arbiter at any level of hierarchy. The application of
the scientific method is a human activity depending on abstraction, and thus differently
motivated people may come up with different solutions or analyses. The various types of
knowledge employed in an engineering project, including the scientific method, but also
including political, mathematical, aesthetic, legal, and many other forms of knowledge, are
human responses to a cultural situation. Joy and fulfillment are enhanced in engineering work
when these cultural connections are understood. These concepts can be incorporated into
engineering courses, in particular, into a linear circuits course.
Bibliography
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http://www.oxforddictionaries.com/us/definition/american_english/science
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http://www.oxforddictionaries.com/us/definition/american_english/scientific-method
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http://www.oxforddictionaries.com/us/definition/american_english/engineering
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